Problem: Rewrite as a simplified fraction. ${0.7\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 74.4444...\\ 10x &= 7.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 67}$ ${x = \dfrac{67}{90}} $